"Investors are going to expect the high level of growth to continue," says Marshal Cohen, chief industry analyst at NPD.

In lululemon's case, this means that the new CEO must have a good understanding of a "lifestyle" company, but also know how to create product and have financial acuity, he says.

Lululemon is in a competitive arena "where price makes a difference," Cohen says. The new leader will have to reinforce that lululemon apparel is worth the money it costs. "It's going to make their product really have to earn those prices, which means the leader must be creative in how to deliver the same for less or deliver even more so that you can stay at those higher prices."

"This is not going to be easy to find," Cohen says. The new CEO must be "someone that comes from wide-spectrum business" with great leadership skills, he adds, noting that the perfect candidate will not be cheap.

The resignation of lululemon's CEO was announced at the same time as its first-quarter results on Monday. The numbers beat analysts' expectations, despite the Luon pants fiasco in March. Net income rose 1.5% to $47.3 million, or 32 cents a share, from a year earlier.

"The plans have been laid for the next five years and a vision for the next 10 years," Day, 51, said in a statement on Monday. "I feel that the timing is now right to bring in the next CEO candidate who will drive that 10-year vision."